<p style='text-indent:20px;'>Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard robust controller designs can compensate small uncertainties if they can be qualified as a coprime factor perturbation of the plant. We show that for the linearized Navier-Stokes equations, a linearization error can be expressed as a coprime factor perturbation and that this perturbation smoothly depends on the size of the linearization error. In particular, improving the linearization makes the perturbation smaller so that, eventually, standard robust controller will stabilize the system.</p>

中文翻译：

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互质因子扰动的收敛对于 Oseen 系统的稳健稳定

<p style='text-indent:20px;'>基于线性化的不可压缩流控制器已被证明在理论和模拟中有效。为了在数值上实现这样的控制器，必须对无限维系统进行线性化和离散化。不可避免的一致性错误给控制器模型增加了一个很小但很关键的不确定性，这可能会导致它失败，尤其是当涉及到观察者时。标准鲁棒控制器设计可以补偿小的不确定性，如果它们可以被认定为工厂的互质因子扰动。我们表明，对于线性化的 Navier-Stokes 方程，线性化误差可以表示为互质因子扰动，并且这种扰动平滑地取决于线性化误差的大小。特别是，